It's a 4X in space.

There are Fleets and Flotillas (so those names are taken). Those are composed of Battle Groups (a unit containing 1 flagship, 1-2 battleships and 4-8 smaller ships like frigates and destroyers).

Now, Battle Group is quite a longish name... I would not mind something shorter and/or sounding better. Especially since those would be used a lot (and I'm not sure an abbreviation "GBs" or "B.G.s" would sound good and intuitive).

I was thinking of Squadrons, but those sound like "Fighter Squadron", definitely not like somethining containing battleships...

Flight. 

Armada.

Try the following names with your game lore names:

-Corps

-Vanguard

-Legion

-Division

-Service

If "Battle Group" is a good name but too long, how about just "Group"?

Maybe a combat team? 

deployment, detachment

How about a different language like German? "Gefechtsverband" or "Bataillion"? Sounds much more dangerous, because it sounds stranger and for most German still sounds very aggressive and can be marketed well.

sounds nice to me 

If this aggregation has a flagship it should also have a particularly high ranking commander (an admiral?), so it would be natural to consider it that officer's fairly autonomous "command" or "force".